Abstract
Several popular, suboptimal algorithms for bit decoding of binary block codes such as turbo decoding, threshold decoding, and message passing for LDPC, were developed almost as a common sense approach to decoding of some specially designed codes. After their introduction, these algorithms have been studied by mathematical tools pertinent more to computer science than the conventional algebraic coding theory. We give an algebraic description of the optimal and suboptimal bit decoders and of the optimal and suboptimal message passing. We explain exactly how suboptimal algorithms approximate the optimal, and show how good these approximations are in some special cases.
This work was supported by the 1999 German-American Networking Research Grant given by the national academies of engineering of Germany and the USA.
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© 2001 Springer-Verlag New York, Inc.
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Offer, E., Soljanin, E. (2001). An Algebraic Description of Iterative Decoding Schemes. In: Marcus, B., Rosenthal, J. (eds) Codes, Systems, and Graphical Models. The IMA Volumes in Mathematics and its Applications, vol 123. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0165-3_15
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DOI: https://doi.org/10.1007/978-1-4613-0165-3_15
Publisher Name: Springer, New York, NY
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